Max number of electrons when only n is given

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In an online source I found the rule that "The max number of electrons in the nth shell is 2n^2."

1. Is this accurate?
2. Can this be used in the homework problems that discuss how many electrons are present when only n is given? (ex. n = 2 --> 2(2^2) --> 8 electrons present)?

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"The max number of electrons in the nth shell is 2n^2."

To answer the first question: Yes, this is accurate. To illustrate this, let's take the 2nd energy level. The value of "n," or the energy level is two. We know that s has 3 orbitals (px, py, pz), which are perpendicular to each other and lie along the x-, y-, and z-axes. Also, as explained by the Pauli Exclusion Principle, each orbital can hold a maximum of 2 electrons. So to calculate the maximum number of electrons, we have to account for both the s and p subshells. The s sublevel has one orbital (with a maximum of 2 electrons) and for the p sublevel, we know that p has 3 orbitals and a maximum of 2 electrons in each orbital. So, we can figure out that the maximum number of electrons is (1x2) + (3x2) = 8. Using the "2n^2" equation, we do the following: "2 (2)^2 = (2x4) = 8 electrons." But it is important to remember that this equation only applies to finding the maximum number of electrons occupying that specific energy level, and not a specific orbital.

For the second question: It is possible to use the equation "2n^2" to figure out the maximum number of electrons present, but remember this is the maximum number for the energy level. Therefore, we cannot use this formula to figure the number of electrons that can occupy a specific orbital, like 3d or 1s. To illustrate this, we look at 1.57 part (c), where it asks "how many electrons can occupy the 1s-orbital?" Here, we are finding the maximum number of electrons in the 1s-orbital, not the 1st energy level. Therefore, we cannot use the "2n^2" formula here. If it were asking "how many electrons can occupy the 1st energy level?" or "find the maximum number of electrons when n=1," then we could apply this formula.

This description might be a little confusing, so please let me know if you need any further clarification! Hope this helped in understanding!